I have just drank a couple of my Coopers IPA that are a little lively when opened and taste a wee-bit too bitter. Would leaving the brew for any further length of time solve this problem, as the bottles have only sat for one week. All suggestions would be greatly appreciated.

The overcarbonation could come from the beer not completely fermenting out before bottling, adding too much carbonation sugar, not getting the sugar mixed in evenly, or a contaminating wild yeast. None of those will get any better and may get worse. If its because the beer wasn't evenly mixed, then some bottles may be overcarbonated, some may be just right, and some undercarbed.

Bitterness will decrease with time. Since the beer has only been in the bottles for a week, then the yeast probably hasn't settled completely. As it settles, it will bring some of the bitterness down with it and also leave a smoother bitterness behind. This is sometimes known as green beer, and you may find that the beer really starts to peak after about 2 months from the brew date. If the beer is still too bitter, bitterness does continue to fade over time, so you may just need to wait until it's where you like it.